EXAMPLES. OPERATION. 1. What is the area of a circle whose diameter is 6? We first square the diameter, giving 36, which we then multiply by the decimal .7854: the product is the area of the circle. .7854 x 36=28.2744 Ans. 28.2744 2. What is the area of a circle whose diameter is 10? Ans. 78.54. 3. What is the area of a circle whose diameter is 7? Ans. 4. How many square yards in a circle whose diameter is 3 feet? Ans. 1.069016+. 288. To find the surface of a sphere, Multiply the square of the diameter by 3.1416. EXAMPLES. B 1. What is the surface of a sphere whose diameter is 12? We simply multiply the decimal 3.1416 by the square of the diameter: the product is the surface. OPERATION. Ans. 452.3904 287. What is a sphere? What is a diameter? What is a radius? 288. How do you find the surface of a sphere? 2. What is the surface of a sphere whose diameter is 7? Ans. 153.9384. 3. Required the number of square inches in the surface of a sphere whose diameter is 2 feet or 24 inches. Ans. 4. Required the area of the surface of the earth, its mean diameter being 7918.7 miles. Ans. 196996571.722104 sq. miles. 289. To find the solidity of a sphere, Multiply the surface by the diameter and divide the product by 6, the quotient will be the solidity. EXAMPLES. 1. What is the solidity of a sphere whose diameter 2. What is the solidity of a sphere whose diameter is 4? Ans. 33.5104. Ans. 3. What is the solidity of a sphere whose diameter is 14 inches? 4. What is the solidity of the earth, its mean diameter being 7918.7 miles? Ans. 259992792079.860+. 5. What is the solidity of a sphere whose diameter is 6 feet? Ans. 113.0976 S. ft. 289. How do you find the solidity of a sphere? Multiply the perimeter of the base by the perpendicular height, and the product will be the convex surface. EXAMPLES. 1. What is the convex surface of a prism whose base is bounded by five equal sides, each of which is 35 feet, the altitude being 26 feet? Ans. 4550 Sq. ft. 2. What is the convex surface when there are eight equal sides, each 15 feet in length, and the altitude is 12 feet? Ans. 1440 Sq.ft. 291. To find the solid content of a prism, Multiply the area of the base by the altitude, and the product will be the content. EXAMPLES. 1. What is the content of a square prism, each side of the square which forms the base being 15, and the altitude of the prism 20 feet? We first find the area of the square which forms the base, and then multiply by the altitude. OPERATION. 15=225 Ans. 4500 290. What is a prism? What is the perimeter of its base? What is its convex surface? How do you find the convex surface of a prism? 291. How do you find the solid content of a prism? 2. What is the solid content of a cube each side of which is 24 inches? Ans. 13824 solid in. 3. How many cubic feet in a block of marble of which the length is 3 feet 2 inches, breadth 2 feet 8 inches, and height or thickness 2 feet 6 inches? Ans. 21 solid ft. 4. How many gallons of water will a cistern contain whose dimensions are the same as in the last example? Ans. 1572 gal. 5. Required the solidity of a triangular prism whose height is 10 feet, and area of the base 350? Ans. 3500. 292. A cylinder is a round body with circular ends. The line EF is called the axis or altitude, and the circular surface the convex surface of the cylinder. C 293. To find the convex surface, Multiply the circumference of the base by the altitude, and the product will be the convex surface. EXAMPLES. 1. What is the convex surface of a cylinder, the diameter of whose base is 20 and the altitude 50? We first multiply the diameter by 3.1416, which gives the circumference of the base. Then multiplying by the altitude, we obtain the convex surface. OPERATION. 3.1416 20 62.8320 50 Ans. 3141.6000 292. What is a cylinder? What is the axis or altitude? What is the convex surface? 293. How do you find the convex surface? 2. What is the convex surface of a cylinder whose altitude is 14 feet and the circumference of its base 8 feet 4 inches? Ans. 116.666+ Sq. ft. 3. What is the convex surface of a cylinder, the diameter of whose base is 30 inches and altitude 5 feet? Ans. 5654.88 Sq. in. 4. What is the convex surface of a cylinder, the diameter of whose base is 20 and altitude 50 feet? Ans. 294. To find the solidity of a cylinder, 3141.6Sq.ft. Multiply the area of the base by the altitude: the product will be the solid content. EXAMPLES. 1. Required the solidity of a cylinder of which the altitude is 12 feet, and the diameter of the base 15 feet. 2. What is the solidity of a cylinder, the diameter of whose base is 20 and the altitude 29?. Ans. 9110.64. 3. What is the solidity of a cylinder, the diameter of whose base is 12 and the altitude 30? Ans. 3392.928. 4. What is the solidity of a cylinder, the diameter of whose base is 16 and altitude 9? Ans. 5. What is the solidity of a cylinder, the diameter of whose base is 50 and altitude 15? Ans. 29452.5. 294. How do you find the solidity of a cylinder? |